A long time behavior for gradient-like systems under a weak angle condition

Tóm tắt

We study the long time behavior of solutions of gradient-like systems that admit a strict Lyapunov function. In a recent paper of Merlet and Nguyen [11], the authors showed that if the Lyapunov function satisfies the Kurdyka-Lojasiewicz inequality then the convergence result can be obtained by the angle condition. In this paper, we extend this result by taking a weaker angle condition which was proposed by Huang in [6]. The convergence rates are also obtained under some additional hypotheses.